Spin and pseudospin symmetries of the Dirac equation with confining central potentials

We derive the node structure of the radial functions which are solutions of the Dirac equation with scalar $S$ and vector $V$ confining central potentials, in the conditions of exact spin or pseudospin symmetry, i.e., when one has $V=\pm S+C$, where $C$ is a constant. We show that the node structure for exact spin symmetry is the same as the one for central potentials which go to zero at infinity but for exact pseudospin symmetry the structure is reversed. We obtain the important result that it is possible to have positive energy bound solutions in exact pseudospin symmetry conditions for confining potentials of any shape, including naturally those used in hadron physics, from nuclear to quark models. Since this does not happen for potentials going to zero at large distances, used in nuclear relativistic mean-field potentials or in the atomic nucleus, this shows the decisive importance of the asymptotic behavior of the scalar and vector central potentials on the onset of pseudospin symmetry and on the node structure of the radial functions. Finally, we show that these results are still valid for negative energy bound solutions for anti-fermions.Comment: 7 pages, uses revtex macro

Transmission coefficient and two-fold degenerate discrete spectrum of spin-1 bosons in a double-step potential

The scattering of spin-1 bosons in a nonminimal vector double-step potential is described in terms of eigenstates of the helicity operator and it is shown that the transmission coefficient is insensitive to the choice of the polarization of the incident beam. Poles of the transmission amplitude reveal the existence of a two-fold degenerate spectrum. The results are interpreted in terms of solutions of two coupled effective Schr\"{o}dinger equations for a finite square well with additional $\delta$-functions situated at the borders.Comment: arXiv admin note: substantial text overlap with arXiv:1203.119

New solutions of the D-dimensional Klein-Gordon equation via mapping onto the nonrelativistic one-dimensional Morse potential

New exact analytical bound-state solutions of the D-dimensional Klein-Gordon equation for a large set of couplings and potential functions are obtained via mapping onto the nonrelativistic bound-state solutions of the one-dimensional generalized Morse potential. The eigenfunctions are expressed in terms of generalized Laguerre polynomials, and the eigenenergies are expressed in terms of solutions of irrational equations at the worst. Several analytical results found in the literature, including the so-called Klein-Gordon oscillator, are obtained as particular cases of this unified approac

Effect of Al doping on the optical phonon spectrum in Mg(1-x)Al(x)B(2)

Raman and infrared absorption spectra of Mg(1-x)Al(x)B(2) have been collected for 0<x<0.5 in the spectral range of optical phonons. The x-dependence of the peak frequency, the width and the intensity of the observed Raman lines has been carefully analized. A peculiar x-dependence of the optical modes is pointed out for two different Al doping ranges. In particular the onset of the high-doping structural phase previously observed in diffraction measurements is marked by the appearence of new spectral components at high frequencies. A connection between the whole of our results and the observed suppression of superconductivity in the high doping region is established

Tailoring Graphene with Metals on Top

We study the effects of metallic doping on the electronic properties of graphene using density functional theory in the local density approximation in the presence of a local charging energy (LDA+U). The electronic properties are sensitive to whether graphene is doped with alkali or transition metals. We estimate the the charge transfer from a single layer of Potassium on top of graphene in terms of the local charging energy of the graphene sheet. The coating of graphene with a non-magnetic layer of Palladium, on the other hand, can lead to a magnetic instability in coated graphene due to the hybridization between the transition-metal and the carbon orbitals.Comment: 5 pages, 4 figure

On the regular-geometric-figure solution to the N-body problem

The regular-geometric-figure solution to the $N$-body problem is presented in a very simple way. The Newtonian formalism is used without resorting to a more involved rotating coordinate system. Those configurations occur for other kinds of interactions beyond the gravitational ones for some special values of the parameters of the forces. For the harmonic oscillator, in particular, it is shown that the $N$-body problem is reduced to $N$ one-body problems.Comment: To appear in Eur. J. Phys. (5 pages

Disordered Kondo Nanoclusters: Effect of Energy Spacing

Exact diagonalization results for Kondo nanoclusters alloyed with mixed valence impurities show that tuning the {\it energy spacing}, $\Delta$, drives the system from the Kondo to the RKKY regime. The interplay of $\Delta$ and disorder gives rise to a $\Delta$ versus concentration T=0 phase diagram very rich in structure, where regions with prevailing Kondo or RKKY correlations alternate with domains of ferromagnetic order. The local Kondo temperatures, $T_K$, and RKKY interactions depend strongly on the local environment and are overall {\it enhanced} by disorder, in contrast to the hypothesis of ``Kondo disorder'' single-impurity models.Comment: 4pages 4 figuresDisordered Kondo Nanoclusters: Effect of Energy Spacin